Date Published: February 21, 2018
Publisher: Public Library of Science
Author(s): Eric Njuki, Boris E. Bravo-Ureta, Christopher J. O’Donnell, Joshua L Rosenbloom.
Random fluctuations in temperature and precipitation have substantial impacts on agricultural output. However, the contribution of these changing configurations in weather to total factor productivity (TFP) growth has not been addressed explicitly in econometric analyses. Thus, the key objective of this study is to quantify and to investigate the role of changing weather patterns in explaining yearly fluctuations in TFP. For this purpose, we define TFP to be a measure of total output divided by a measure of total input. We estimate a stochastic production frontier model using U.S. state-level agricultural data incorporating growing season temperature and precipitation, and intra-annual standard deviations of temperature and precipitation for the period 1960–2004. We use the estimated parameters of the model to compute a TFP index that has good axiomatic properties. We then decompose TFP growth in each state into weather effects, technological progress, technical efficiency, and scale-mix efficiency changes. This approach improves our understanding of the role of different components of TFP in agricultural productivity growth. We find that annual TFP growth averaged 1.56% between 1960 and 2004. Moreover, we observe substantial heterogeneity in weather effects across states and over time.
According to the United States National Climate Assessment: “Climate change poses a major challenge to U.S. agriculture because of the critical dependence of the agricultural system on climate and because of the complex role agriculture plays in rural and national social and economic systems” . This challenge is of major concern given the critical role that this country plays in global food production and world food markets. It is noteworthy that in 2016, the U.S. generated approximately 35% of global corn supply, 33% of global soybeans and close to 33% of global dairy products . Thus, understanding how to manage the agricultural sector in the face of climate change will enable the development of effective strategies aimed at coping with this challenge.
This section presents the methodology that is used to characterize the production technology. This article distinguishes between the production technology and environmental factors that impact production outcomes. To be specific, a technology is defined as “…a technique, method or system for transforming inputs into outputs” . On the other hand, environmental factors consist of all exogenous variables that are physically involved in the production process but that are beyond the control of the firm. In the context of this article, the environmental factors of relevance are weather variables and time-invariant regional features such as topography. The set of all technologies available in period t is referred to as the period-t technology set. In addition, the set of all input-output combinations that are feasible using a given technology set in a given period in a given environment is referred to as a period-and-environment-specific production possibilities set. For example, in mathematical terms, the set of output-input combinations that can be produced using the period-t technology set in environment z is given as:
The data used consists of indices of farm output and inputs across the 48 contiguous states of the U.S. and is developed by the Economic Research Service (ERS) of the U.S. Department of Agriculture . Several authors have used similar data to analyze different productivity issues [20,27,29,32,33]. The aggregate output index is constructed by the ERS from measures of physical quantities of livestock, crop and other outputs, and their respective state-level market prices. The input indices consist of land, labor, capital and intermediate materials, all calculated by the ERS. Details concerning the construction of the input and output indices are elaborated in Ball et al. [27,33,34]. This article utilizes the full data set for the 45-year period between 1960 and 2004; thus, the total number of observations is 2,160. Table 1 provides a summary of the descriptive statistics of the variables used in the stochastic production frontier analysis. The complete dataset used in this analysis is included as S1 File.
Prior to discussing our results, we acknowledge possible concerns regarding the potential for endogeneity in stochastic production frontier models [47–49]. A possible source of endogeneity is that input choices may be driven by weather outcomes. Verbeek  and O’Donnell  claim that if at least one of the explanatory variables is an I(1) process and the dependent and explanatory variables are cointegrated, then least squares estimators for the slope parameters will be super-consistent even if some of the variables are endogenous. We tested for unit roots using the panel unit root test of Maddala and Wu . Using 4 lags, we failed to reject the null hypothesis of a unit root at the 5% level of significance for the dependent variable, and the explanatory variables; land, labor, irrigation, precipitation and temperature. We then conducted a Pedroni  test and concluded that the variables are cointegrated. Maximum likelihood estimates of the parameters of the stochastic production frontier model are provided in Table 2.
This article builds upon previous studies that have analyzed total factor productivity (TFP) trends in U.S. agriculture [27,29,33]. We extend these recent analyses by explicitly introducing weather variables into a stochastic production frontier model. Consequently, we provide new results concerning TFP growth in U.S. agriculture in a way that accounts for the effect of weather variation. Another salient contribution of this paper is the use of the general TFP index that was proposed in O’Donnell , which satisfies a suite of economically relevant axioms from index theory and makes it possible to derive a complete decomposition of TFP change.